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Modified Landau levels, damped harmonic oscillator, and two-dimensional pseudo-bosons
Twareque Ali S., Bagarello F., Gazeau J.-P.
Journal of Mathematical Physics 51 (2010) 123502 - http://hal.archives-ouvertes.fr/hal-00739315
Physique/Physique mathématique
Mathématiques/Physique mathématique
Modified Landau levels, damped harmonic oscillator, and two-dimensional pseudo-bosons
S. Twareque Ali, F. Bagarello, J.-P. Gazeau1
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
APC - UMR 7164, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, case postale 7020, F-75205 Paris Cedex 13
In a series of recent papers, one of us has analyzed in some details a class of elementary excitations called pseudo-bosons. They arise from a special deformation of the canonical commutation relation [a, a†] = 11, which is replaced by [a, b] = 11, with b not necessarily equal to a†. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e., a damped harmonic oscillator.

Journal of Mathematical Physics (J. Math. Phys.)
Publisher American Institute of Physics (AIP)
ISSN 0022-2488 
Articles dans des revues avec comité de lecture

boson systems – harmonic oscillators – Landau levels – Solutions of wave equations: bound states – Boson systems